Reversing the Question

Don Steward posted this on Sunday. Like Don, I really like this task and also think it has a certain Malcolm Swan je ne sais quoi about it.

I showed only the top part to my 6th graders, and I gave them 2 minutes to write down what they notice.

In addition to noticing the given information, the students also mentioned:

It takes a lot of grams to make a sponge cake.

A kilogram must have a lot of grams in it.

The unit of measurement is changed in the cake and in the big bag.

This problem doesn’t have a question.

The sponge cake has no price.

There is frosting on the cake.

You need to change the measurements first (kg – g)

The cake weighs more.

The cake is really small and the flour is really big.

Not much information and there’s no question.

There is no question. The weight of the bag is in kg but the flour it takes for the cake is in g.

You have to convert 24 kg to grams.

It uses only very little of the flour.

I gave them another 2 minutes to write down what they wonder.

How much the sponge cake costs.

How many sponge cakes can you make.

How big is the sponge cake.

How to convert from kg to g.

If the sponge cake is good.

24 kg is <, =, or > 150 g.

What we are going to have to solve.

Is the question going to be about if there’s enough flour or is it going to make us change it from kg to g.

How much 24 kilograms is in pounds.

How many grams are in a kilogram?

How many krumkakes can you make with the bag of flour.

How long will it take for the cake to be ready.

What a sponge cake is and what the recipe is for the cake.

How much flour is left.

What flavor is the cake. (Sorry. I’m hungry!)

What you’re wondering that I’m wondering about.

What the question is, and if there are more ingredients.

If we will have to find the price for the sponge cake, or maybe we have to find out how much half as much flour is worth.

Then we moved on to next part of providing questions that would go with the calculations. This was so very tough for my kids. While 21 of 31 kids could come up with the correct question for part (a), they were lost with what to write for the other three parts.

reverse the question 2

Because we didn’t care what the numerical answers were, the kids didn’t do any calculations, instead they were supposed to focus on the operation(s) in each problem and decide on the question that would prompt a specific operation.

The most common question for part (b) was, “How much does 1 kg of flour cost?” (I’d swapped out £ for $.)

Then my next step would be for them to go ahead and use a calculator to get the numerical answers. They will see that for part (b), 24 divided by 21.50 equals approximately 1.12. And if 1.12 were the cost for 1 kg of flour, then 24 kg of flour should cost more than $24. But, wait. We already know that the bag of flour costs $21.50. Hopefully they’ll arrive at this contradiction on their own, and re-think their question.

We’ll then attach the units to the numbers accordingly and let the conversations continue. When kids tell me that they will calculate two numbers using operation w, I always follow up with, What does your answer mean? What unit or units does it carry?

Too often kids have trouble with word problems. Too often they don’t know what to do with two numbers let alone a bunch of numbers. They guess at division when one number is big and one is small. They add when they see two fractions. They multiply because that was how they solved the last word problem.

I will also do this with my 8th graders because I suspect they will have trouble too. And this is exactly the kind of trouble we need to get into. Now rather than later. This task gets them thinking about ratios — which is like the most important math thing in all of the math things.

Steward is exactly right about this task. And I’m thankful he shared.

It was used as a fine example of how reversing the question can often lead to a more challenging task.

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6 Comments

  1. Ray O'Brien
    Posted March 4, 2015 at 6:57 pm | Permalink

    Great example of how to open up the game or the conversation instead of closing it with one answer. You give your kids a chance to solve other problems by letting them “write” their own problems for the answers.

  2. Posted March 4, 2015 at 7:10 pm | Permalink

    I do like this way of looking at stuff, and I really like that the kids wanted to have the same weight units for both items.
    I found this in Eureka Math grade 3
    ———–
    4 L 342 mL + 2 L 214 mL
    3 kg 296 g + 5 kg 326 g
    ———–
    and I wept !!!!!

    • Fawn
      Posted March 4, 2015 at 8:11 pm | Permalink

      Oh my God. If I saw that in any textbook, I’d cry too. The sad thing is somehow that question passed inspection. We are all entitled to stupid ideas, but when we have collaborators cheering us to our carry out our stupid ideas, that’s just criminal. Now I want to punch someone in the face. Thanks, Howard.

  3. Posted March 5, 2015 at 8:53 am | Permalink

    Great problem, Fawn! It illustrates the how important units are in solving any “real world” problem. It reminds me of using dimensional analysis to change a miles per hour (miles/hour) quantity into a feet per second (feet/sec) quantity by multiplying by 1 in the form of equivalent quantities of 1 hour/60 min, 1 min/60 sec, 5280 ft/1 mile. For some reason that I’ve never figured out, this procedure has the fancy name of “dimensional analysis”. I’d rather call it a creative use of the identity property of multiplication.

    I love Don Steward’s blog, but I don’t think I can subscribe to it through email and therefore forget to check it out on a regular basis. Thanks for sharing this! I’m going to post it to my own blog http://www.watsonmath, which has one, maybe two followers.

  4. Tina Cardone
    Posted January 18, 2016 at 6:58 am | Permalink

    Hello! This post was recommended for MTBoS 2015: a collection of people’s favorite blog posts of the year. We would like to publish an edited volume of the posts and use the money raised toward a scholarship for TMC. Please let us know by responding via email to tina.cardone1@gmail.com whether or not you grant us permission to include your post. Thank you, Tina and Lani.

  5. Posted January 17, 2017 at 11:17 pm | Permalink

    Great site! I am loiving it!! Will come back again. I amm taking your feeds also

    Here is my wwebsite – fun with escorts (Roseann)

9 Trackbacks

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